In our recent theoretical work, we have provided a complete 1-D theory for restoring signals with finite rate of innovations (FRI) from sparse Fourier measurements using low-rank Fourier interpolation. In this work, we are expanding this theory for restoring common sparse signals where the singularity of the FRI signals is at the same position, while the unknown weights are different for each channel. We consider two situations: one for the same Fourier sampling pattern, which corresponds to the multiple measurement vector problems (MMV), and the other for different sampling patterns.
We will derive performance guarantees: one for the algebraic guraantee and the other for probabilistic guarantee from randomly sampled Fourier measurements. We will discuss the relationship between the newly derived bounds and those of multiple signal classification (MUSIC) algorithm and single channel low-rank Fourier interpolation.

We present a methodology for the optimization of sampling schemes in diffuse optical tomography (DOT). The proposed method exploits singular value decomposition (SVD) of the sensitivity matrix, or weight matrix, in DOT. Two mathematical metrics are introduced to assess and determine the optimum source–detector measurement configuration in terms of data correlation and image space resolution. The key idea of the work is to weight each data measurement, or rows in the sensitivity matrix, and similarly to weight each unknown image basis, or columns in the sensitivity matrix, according to their contribution to the rank of the sensitivity matrix, respectively. The proposed metrics offer a perspective on the data sampling and provide an efficient way of optimizing the sampling schemes in DOT. We evaluated various acquisition geometries often used in DOT by use of the proposed metrics. By iteratively selecting an optimal sparse set of data measurements, we showed that one can design a DOT scanning protocol that provides essentially the same image quality at a much reduced sampling.

In this paper, we review joint sparse recovery based reconstruction approach for inverse scattering problems that can solve the nonlnear inverse scattering probleme without linearization or iterative Green's function update. The main idea is to exploit the common support conditions of anomalies during multiple illumination or current injections, after which unknown potential or field can be estimated using recursive integral equation relationship. Explicit derivation for electric impedance tomography and diffuse optical tomography are discussed.

Localization microscopy such as STORM/PALM can achieve a nanometer scale spatial resolution by iteratively localizing fluorescence molecules. It was shown that imaging of densely activated molecules can accelerate temporal resolution which was considered as major limitation of localization microscopy. However, this higher density imaging needs to incorporate advanced localization algorithms to deal with overlapping point spread functions (PSFs). In order to address this technical challenges, previously we developed a localization algorithm called FALCON1, 2 using a quasi-continuous localization model with sparsity prior on image space. It was demonstrated in both 2D/3D live cell imaging. However, it has several disadvantages to be further improved. Here, we proposed a new localization algorithm using annihilating filter-based low rank Hankel structured matrix approach (ALOHA). According to ALOHA principle, sparsity in image domain implies the existence of rank-deficient Hankel structured matrix in Fourier space. Thanks to this fundamental duality, our new algorithm can perform data-adaptive PSF estimation and deconvolution of Fourier spectrum, followed by truly grid-free localization using spectral estimation technique. Furthermore, all these optimizations are conducted on Fourier space only. We validated the performance of the new method with numerical experiments and live cell imaging experiment. The results confirmed that it has the higher localization performances in both experiments in terms of accuracy and detection rate.

In this paper, a novel patch-based signal processing algorithm for motion estimated/compensated compressed
sensing dynamic MR imaging is proposed. More specifically, we impose a non-convex patch-based low-rank
penalty that exploits self-similarities within the images. This penalty is shown to favor capturing geometric
features such as edges rather than reconstructing the background noises. To solve the resulting non-convex
optimization problem, we propose a globally convergent concave-convex procedure (CCCP) using convex conju-
gate, which has closed form solution at each sub-iteration. Experimental results demonstrate that the proposed
algorithm outperforms the existing ones.

Recently, there has been increased interest in the usage of neuroimaging techniques to investigate what happens
in the brain at rest. Functional imaging studies have revealed that the default-mode network activity is disrupted
in Alzheimer's disease (AD). However, there is no consensus, as yet, on the choice of analysis method for the
application of resting-state analysis for disease classification. This paper proposes a novel compressed sensing
based resting-state fMRI analysis tool called Sparse-SPM. As the brain's functional systems has shown to have
features of complex networks according to graph theoretical analysis, we apply a graph model to represent a
sparse combination of information flows in complex network perspectives. In particular, a new concept of spatially
adaptive design matrix has been proposed by implementing sparse dictionary learning based on sparsity. The
proposed approach shows better performance compared to other conventional methods, such as independent
component analysis (ICA) and seed-based approach, in classifying the AD patients from normal using resting-state
analysis.

The goal of this paper is to develop novel algorithms for inverse scattering problems such as EEG/MEG, microwave
imaging, and/or diffuse optical tomograpahy, and etc. One of the main contributions of this paper is
a class of novel non-iterative exact nonlinear inverse scattering theory for coherent source imaging and moving
targets. Specifically, the new algorithms guarantee the exact recovery under a very relaxed constraint on the
number of source and receivers, under which the conventional methods fail. Such breakthrough was possible
thanks to the recent theory of compressive MUSIC and its extension using support correction criterion, where
partial support are estimated using the conventional compressed sensing approaches, then the remaining supports
are estimated using a novel generalized MUSIC criterion. Numerical results using coherent sources in
EEG/MEG and dynamic targets confirm that the new algorithms outperform the conventional ones.

This paper describes a novel quantitative phase microscopy based on a simple self-referencing scheme using
Michelson interferometry. In order to achieve the homogeneous reference field for accurate phase measurement,
the imaging field-of-view (FOV) is split onto the sample and homogenous background areas. The reference field
can be generated by rotating the relative position of the sample and homogenous background in the object arm.
Furthermore, our system is realized using an extended depth-of-field (eDOF) optics, which allows quantitative
phase measurement for an increase of the depth-of-field without moving objective lens or specimen. The proposed
method is confirmed by experimental results using various samples such as polystyrene beads and red blood cells
(RBCs).

Inverse scattering refers the retrieval of the unknown constitutive parameters from measured scattered wave
fields, and has many applications such as ultrasound imaging, optics, T-ray imaging, radar, and etc. Two
distinct imaging strategies have been commonly used: narrow band inverse scattering approaches using a large
number of transmitters and receivers, or wideband imaging approaches with smaller number of transmitters and
receivers. In some biomedical imaging applications, the limited accessibility of scattered fields using externally
located antenna arrays usually prefers the wideband imaging approaches. The main contribution of this paper is,
therefore, to analyze the wideband inverse scattering problem from compressive sensing perspective. Specifically,
the mutual coherence of the wideband imaging geometry is analyzed, which reveals a significant advantage to
identify the sparse targets from very limited number of measurements.

Near-infrared spectroscopy (NIRS) can be employed to investigate brain activities associated with regional changes of the oxy- and deoxyhemoglobin concentration by measuring the absorption of near-infrared light through the intact skull. NIRS is regarded as a promising neuroimaging modality thanks to its excellent temporal resolution and flexibility for routine monitoring. Recently, the general linear model (GLM), which is a standard method for functional MRI (fMRI) analysis, has been employed for quantitative analysis of NIRS data. However, the GLM often fails in NIRS when there exists an unknown global trend due to breathing, cardiac, vasomotion, or other experimental errors. We propose a wavelet minimum description length (Wavelet-MDL) detrending algorithm to overcome this problem. Specifically, the wavelet transform is applied to decompose NIRS measurements into global trends, hemodynamic signals, and uncorrelated noise components at distinct scales. The minimum description length (MDL) principle plays an important role in preventing over- or underfitting and facilitates optimal model order selection for the global trend estimate. Experimental results demonstrate that the new detrending algorithm outperforms the conventional approaches.

Recently, a model based dynamic imaging algorithm called k-t BLAST/SENSE has drawn significant attentions from MR imaging community due to its improved spatio-temporal resolution for dynamic MR imaging. In our previous work, we proved that k-t BLAST/SENSE can be derived as the first step of FOCal Underdetermined System Solver (FOCUSS) that exploits the sparsity of x-f support. Furthermore, the newly derived algorithm called k-t FOCUSS can be shown optimal from compressed sensing perspective. In this paper, the k-t FOCUSS algorithm is extended to radial trajectory. More specifically, the
radial data are transformed to Cartesian domain implicitly during
the FOCUSS iterations without explicit gridding to prevent error propagation. Thanks to the implicit gridding that allows fast Fourier transform, we can reduce the computational burden
significantly. Additionally, a novel concept of motion estimation and compensation (ME/MC) is proposed to
improve the performance of the algorithm significantly. In our ME/MC framework, we additionally obtain one reference sinogram with the full view, then the reference signogram is subtracted from all the radial data. Then, we can apply motion estimation/ motion compensation (ME/MC) to improve the final reconstruction. The experimental results show that our new method can provide very high resolution even from very limited radial data set.

Near infrared spectroscopy (NIRS) is a relatively new non-invasive brain imaging method to measure brain
activities associated with regional changes of the oxy- and deoxy- hemoglobin concentration. Typically, functional
MRI or PET data are analyzed using the general linear model (GLM), in which measurements are modeled as a
linear combination of explanatory variables plus an error term. However, the GLM often fails in NIRS if there
exists an unknown global trend due to breathing, cardiac, vaso- motion and other experimental errors. In order
to overcome these problems, we propose a wavelet-MDL based detrending algorithm. Specifically, the wavelet
transform is applied to NIRS measurements to decompose them into global trends, signals and uncorrelated
noise components in distinct scales. In order to prevent the over-fitting the minimum length description (MDL)
principle is applied. Experimental results demonstrate that the new detrending algorithm outperforms the
conventional approaches.

Single particle reconstruction is often employed for 3-D reconstruction of diverse macromolecules. However, the
algorithm requires a good initial guess from a priori information to guarantee the convergence to the correct
solution. This paper describes a novel model free 3-D reconstruction algorithm by employing the symmetry
and sparsity of unknown structure. Especially, we develop an accurate and fully automatic iterative algorithm
for 3D reconstruction of unknown helix structures. Because the macromolecule structure assumes only sparse
supports in real space and the helical symmetry provides several symmetric views from a single micrograph,
a reasonably quality 3-D reconstruction can be obtained from the limited views using the compressed sensing
theory. Furthermore, the correct helix parameters usually provide the maximal variance of the reconstructed
volume, facilitating the parameter estimation. Remarkably, the search space of helix parameter can be drastically
reduced by exploiting the diffraction pattern. With the estimated helix parameter and additional 3-D registration,
the multiple helix segments can be combined for the optimal quality reconstruction. Experimental results using
synthetic and real helix data confirm that our algorithm provides superior reconstruction of 3-D helical structure.

Even though there exists a powerful statistical parametric mapping (SPM) tool for fMRI, similar public domain
tools are not available for near infrared spectroscopy (NIRS). In this paper, we describe a new public domain
statistical toolbox called NIRS-SPM for quantitative analysis of NIRS signals. Specifically, NIRS-SPM statistically
analyzes the NIRS data using GLM and makes inference as the excursion probability which comes from
the random field that are interpolated from the sparse measurement. In order to obtain correct inference, NIRS-SPM
offers the pre-coloring and pre-whitening method for temporal correlation estimation. For simultaneous
recording NIRS signal with fMRI, the spatial mapping between fMRI image and real coordinate in 3-D digitizer
is estimated using Horn's algorithm. These powerful tools allows us the super-resolution localization of the brain
activation which is not possible using the conventional NIRS analysis tools.

This paper describes a novel reconstruction algorithm for microscopy axial tomography, which reconstructs a
3-D volume using multiple tilted views through an off-centered aperture and numerical processing. The main
contribution of this paper is a derivation of novel optimization criterion and algorithm for a cost function
with L1 fidelity term and sparsity constraint. A parallel coordinate descent (PCD) algorithm has been derived
as an efficient optimization methods, which corresponds to iterative application of projection and nonlinear
back-projection using median. Numerical simulation results using synthetic and real microscopy data show
that accurate reconstruction can be obtained rapidly, and interference artifacts from high contrast objects in a
volume can be removed efficiently. Our algorithm is quite general, and can be used for many other tomosynthesis
applications with limited number of views.

Sparse object supports are often encountered in many imaging problems. For such sparse objects, recent theory
of compressed sensing tells us that accurate reconstruction of objects are possible even from highly limited
number of measurements drastically smaller than the Nyquist sampling limit by solving L1 minimization problem.
This paper employs the compressed sensing theory for cryo-electron microscopy (cryo-EM) single particle
reconstruction of virus particles. Cryo-EM single particle reconstruction is a nice application of the compressed
sensing theory because of the following reasons: 1) in some cases, due to the difficulty in sample collection, each
experiment can obtain micrographs with limited number of virus samples, providing undersampled projection
data, and 2) the nucleic acid of a viron is enclosed within capsid composed of a few proteins; hence the support
of capsid in 3-D real space is quite sparse. In order to minimize the L1 cost function derived from compressed
sensing, we develop a novel L1 minimization method based on the sliding mode control theory. Experimental
results using synthetic and real virus data confirm that the our algorithm provides superior reconstructions of
3-D viral structures compared to the conventional reconstruction algorithms.

This paper is concerned about high resolution reconstruction of projection reconstruction MR imaging from
angular under-sampled k-space data. A similar problem has been recently addressed in the framework of compressed
sensing theory. Unlike the existing algorithms used in compressed sensing theory, this paper employs
the FOCal Underdetermined System Solver(FOCUSS), which was originally designed for EEG and MEG source
localization to obtain sparse solution by successively solving quadratic optimization. We show that FOCUSS
is very effective for the projection reconstruction MRI, because the medical images are usually sparse in image
domain, and the center region of the under-sampled radial k-space data still provides a meaningful low resolution
image, which is essential for the convergence of FOCUSS. We applied FOCUSS for projection reconstruction MR
imaging using single coil. Extensive experiments confirms that high resolution reconstruction with virtually free
of angular aliasing artifacts can be obtained from severely under-sampled k-space data.

A novel support vector machine (SVM) classifier incorporating the complexity of fluorescent spectral data is
designed to reliably differentiate normal and malignant human breast cancer tissues. Analysis has been carried
out with parallel and perpendicularly polarized fluorescence data using 36 normal and 36 cancerous tissue samples.
In order to incorporate the complexity of fluorescence spectral profile into a SVM design, the curvature of phase
space trajectory is extracted as a useful complexity feature. We found that the fluorescence intensity peaks at
541nm-620nm as well as the complexity features at 621nm-700nm are important discriminating features. By
incorporating both features in SVM design, we can improve both sensitivity and specificity of the classifier.

In the cryo-EM tomography, the projection and back-projection are essential steps in reconstruction the 3D structure of the virus and macromolecules. Distance driven method (DD) is the latest projection /backprojection algorithm originally employed for x-ray computed tomography. This paper is mainly concerned about employing this algorithm to the cryo-EM tomography for reconstruction performance improvement. Existing algorithms used in cryo-EM are pixel-driven and ray driven projection/backprojection, etc. These methods are generally quite time consuming because of their high computational complexity. Furthermore, interpolation artifacts are usually noticeable when the sufficient view and detector samples are not available. The DD is originally proposed to overcome these drawbacks. The interpolation process in DD is done by calculating the overlap area between the detector and pixel boundaries. This procedure largely removes the interpolation artifacts, and reduces the computational complexity significantly. Furthermore, it guarantees that the projection and backprojection are adjoint to each other - a desired property to guarantee the convergence of the iterative reconstruction algorithm. However, unlike the x-ray computed tomography, the cryo-EM tomography problem generally has limited number of the projections, and projection angles are randomly distributed over 4pi steradian. Therefore, the conventional DD should be modified. Rather than computing the boundary overlap in the previous 3-D DD method, we propose a novel DD algorithm based on volume overlap. CCMV virus model is used as testing example. Results are visualized using AMIRA software. Analysis is made upon the advantages and drawbacks of both the existing approaches and distance driven method.

In this paper we present a polarization based technique for optical sectioning and imaging of multi-layer cell patterns separated by a weakly diffused media. Multi-layer cell pattern is important to study because this type of structure is often used for heterogeneous three dimensional cell culture and bio-chips applications, where information at different depths would be crucial. Functioning of this type of bi-layer or multilayer cell patterns can easily be monitored using polarization based imaging techniques. For polarization based imaging, samples are excited by white light source with different set of band-pass filter and linear polarizer, and images are collected
through corresponding long-pass filters and analyzer by CCD camera. Preliminary experiments are carried out using absorption inhomogeneity separated by a weakly diffused thin polymer layers. Polarized images at various angles are collected at a set of excitation wavelength. Such measurements can identify 3x3 sub-matrix elements out of the full 4x4 sixteen elements of Mueller matrix. In order to enhance the image contrast, the 3x3 Mueller components are further decomposed into diattenuation and depolarization power images. Superficial layer image information is found to be more prominent in the depolarization power images, and diattenuation images provide sub layer information. By comparing the decomposition images at various wavelengths, we can observe sub-layer structures at different depths.

In this paper, we present a fully scalable 3-D overcomplete wavelet video coder that employs a new and highly efficient 3-D lifting structure for adaptive motion compensated temporal filtering (MCTF). Unlike the conventional interframe wavelet video techniques that apply MCTF on the spatial domain video data and then encode the resulting temporally filtered frames using critical sampled wavelet transforms, the scheme proposed in this paper performs first the spatial domain wavelet transform and subsequently applies MCTF for each wavelet band. To overcome the inefficiency of motion estimation in the wavelet domain, the low band shifting method (LBS) is used at both the encoder and decoder to generate an overcomplete representation of the temporal reference frames. A novel interleaving algorithm for the overcomplete wavelet coefficient is proposed that enables optimal sub-pixel accuracy motion estimation implementations. Furthermore, to achieve arbitrary accuracy motion estimation and compensation in the overcomplete wavelet domain with perfect reconstruction, a novel 3-D lifting structure is also introduced. Simulation results shows that the proposed fully scalable 3-D overcomplete wavelet video coder has comparable or better performance (up to 0.5dB) than the previously proposed interframe wavelet coders under the same coding conditions. Several techniques that can further improve the performance of the proposed overcomplete wavelet coding scheme are also discussed.

The unprecedented increase in the level of heterogeneity of emerging wireless networks and the mobile Internet emphasizes the need for scalable and adaptive video solutions both for coding and transmission purposes. However, in general, there is an inherent tradeoff between the level of scalability (e.g., in terms of bitrate range, levels of spatial resolutions, and/or levels of temporal resolutions) and the video-coding penalty incurred by such scalable video schemes as compared to non-scalable coders. In other words, the higher the level of scalability, the lower the overall video quality of the scalable stream that is needed to support the desired scalability level. In [1][2][3], we introduced the notion of TranScaling, which is a generalization of (non-scalable) transcoding. With TranScaling, a scalable video stream covering a given bandwidth range, is mapped into one or more scalable video streams covering different bandwidth ranges. In this paper, we illustrate the benefits of Spatial TranScaling in the context of a recently developed scalable and adaptive inband motion compensated temporal filtering scheme (IBMCTF) [4][5]. We show how using TranScaling, the already high coding efficiency performance of such adaptive IBMCTF schemes can be further improved.

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Journal of Applied Remote SensingJournal of Astronomical Telescopes Instruments and SystemsJournal of Biomedical OpticsJournal of Electronic ImagingJournal of Medical ImagingJournal of Micro/Nanolithography, MEMS, and MOEMSJournal of NanophotonicsJournal of Photonics for EnergyNeurophotonicsOptical EngineeringSPIE Reviews